In the long-gone days of the Soviet Union, the Petrovsky Park arena in the north-west of Moscow was home to the footballing pride of the notorious NKVD, the forerunners of the KGB. Labelled musor – garbage – by their rivals, Dinamo Moscow's heyday was in the 1950s, when fans at the world's only constructivist-designed stadium celebrated the secret police-affiliated side lifting the Soviet championship four times in six seasons. "The whole of Moscow rides stubbornly to Dinamo, forgetting about the rain," wrote poet Lev Oshanin, exaggerating, it must be said, just a touch.

Today, though, in the hard-nosed world of the Russian Premier League, while Dinamo are still based at Petrovsky Park, the club is financed by the state-controlled Bank for Foreign Trade, and maintains only symbolic connections to the security services.

I don't have to stray far from Petrovsky Park, however, to find modern Russia's police team. The offices of FC MVD are just a few corner kicks away from the Dinamo ground, on the other side of Leningradsky Prospekt, the frequently gridlocked stretch of road that cuts through this part of the city before heading north to St Petersburg.

Formed in the summer of 2007, FC MVD, or the "Football Club of the Russian Interior Ministry", to give the outfit their full title, have already seen enough drama to last most teams decades, the side's spectacular rise mirrored only by its recent collapse amid suspicion of large-scale fraud.

The club's first two seasons saw astounding progress, with victory in a Moscow-wide tournament followed by promotion to the second tier of Russian football at the end of last year. "There are even greater triumphs to come," predicted senior police official Nikolai Ovchinnikov after FC MVD had finished top of the Second Division West zone, breaking points and goalscoring records in the process.

I paid my first visit to the club in early March, just before the start of the Russian First Division season, trudging through the slush to a meeting with Alexei Zinin, FC MVD's thirtysomething general director.

"When we began life in the amateur league, there were actual police officers in the team," he told me, pointing to a photograph on his desk of a distinctly overweight bunch of off-duty coppers. "The minister then heard about us and decided to turn the side into a fully fledged Interior Ministry club. He then set us the goal of making it to the Premier League."

Armed with a vastly improved budget, FC MVD duly set about replacing the police officers, bringing in experienced veterans, including former Spartak Moscow wild boy Yuri Kovtun, who still holds the domestic record for yellow cards, as player-manager, and Denis Klyuyev, a former Dinamo Moscow midfielder.

The largely venomous reactions of Russian fans to FC MVD's promotion reflected the widespread antipathy towards the country's underpaid and under-trained police. Posts on fan websites such as soccer.ru ranged from allegations that the club would use its clout to influence results to outrage at its very existence. Others were, admittedly, more light-hearted. "The coppers will just arrest the other side if they are losing at half-time," wrote one.

FC MVD's rapid rise twinned with its high-level backing also led to speculation that Russia could soon have a police side representing it in Europe. But was a successful Russian cops XI really the best thing for the country's already battered world image?

I didn't expect Zinin to react well to the suggestion, but he immediately lit up. "I can assure you," he laughed, "that if we did get to play, say, Manchester United in the Champions League, then we wouldn't worry at all what it might look like or sound like. It would, quite simply, be a dream come true."

I left the team's offices possessed by an almost perverse passion for FC MVD. Like most people here in Russia, I have no reason to be overly fond of the cops, but Zinin's obvious enthusiasm for the game ("I feel real, incredible joy every time Roman Pavlyuchenko scores for Tottenham," he confesses) won me over, and I found myself rooting for the side this spring as they attempted to secure a place in the elite. FC MVD's home gates rarely top 500, a good quarter of the crowd made up of off-duty officers. But low attendances are normal in the kick-and-rush lower leagues.

Despite suspicions that FC MVD, like Soviet-era Dinamo, would enjoy unfair advantages, the side's results were not as good as the Interior Ministry had hoped. An embarrassing pre-season friendly defeat to a convict side was followed by a series of disappointing results once the real campaign got under way. Both Kovtun and Zinin were fired, and former Lokomotiv Moscow assistant Vladimir Eshtrekov accepted an offer to take over. Results began to improve.

And then, this summer, the club's success story shuddered to a halt: dreams of Europe-wide televised encounters with Rooney and co were suddenly no more than a cruel joke, a dark parody of the side's lofty ambitions. The end was as bizarre as it was unexpected.

The roots of the team's downfall reach back to autumn 2008, when transport police at Moscow's Vnukovo airport seized some $15m in various currencies belonging to businessmen from the North Caucasus republic of Dagestan. But the authorities were unable to prove anything and eventually returned the wad of bills to its owners… apart from a million dollars or so. The Dagestanis, believing someone had pulled a fast one, launched legal proceedings.

On 17 June, officers from the Federal Security Service (FSB) raided FC MVD's headquarters, confiscating documents and computers. In a vague statement, the state prosecutor announced that the missing cash could "possibly" have been used to fund the club's activities, based on the fact that one of the team officials was also head of Moscow's transport police. The club denied the allegation. The raid made the news across the country, and there was a certain glee in headlines such as "FC MVD's secret sponsors?".

The team's backers – a group of businesses with close ministry connections – withdrew their sponsorship deals, fearing they would receive the next visit from the FSB. With Russia hit hard by the global economic downturn, the ministry was unable to find replacement funds. As the money ran out, an FC MVD press release declared "We want to play football!" and appealed to the country's leadership to intervene.

Busy with their attempts to revive Russia's superpower status, Vladimir Putin and Dmitry Medvedev failed to respond, and, just over a month after the raid, the club withdrew from the First Division to concentrate on amateur reserve side FC MVD 2.

The team's farewell home game, a 0-0 draw with Siberia's FC Chita, attracted the club's highest-ever crowd, with 3,500 curious spectators cramming into the tiny Domodedovo stadium to check out the lower-league cop side busted by its own colleagues. Then things went quiet.

"No charges have been brought against us," FC MVD chairman Andrei Basov tells me as we sit drinking tea near a Lenin statue in central Moscow. "And not a single person from the club has even been summoned for questioning. We are hoping to get back all the documents taken during the raid very soon, as well as a letter from the state prosecutor stating that we are not guilty.

"It was ridiculous to suspect that the money had been forwarded to the club. Following that logic, every time an ordinary cop takes a bribe, does that cash also go to FC MVD?"

A number of theories have been put forward for the raid. The FSB had been criticised by Putin for failing to tackle corruption, and some believe this was the FSB's zealous response. Others blame infighting within the security services. Basov, a bearded businessman who has been involved with the club since its amateur days, leans towards the latter theory, and tells me that the search of the team's offices was just a way for the FSB "to have it out with us. To prove who was stronger".

Basov remains enthusiastic. "We are doing well in the Moscow Cup," he says of FC MVD 2. "Success in that would give us the chance to enter the third tier of professional football again. If all goes well, God willing, we could be back in the First Division in two years."

I find myself feeling sympathy for Basov and FC MVD, victims, apparently, of forces beyond their control. But short of a lengthy, not to mention hazardous, investigation into the internal workings of Russia's security structures, I am unlikely ever to find out exactly what really went on this summer.

Instead, the FC MVD story is one of the elements that make the modern Russian game so compelling. Russian football, like the country itself, is in flux, and while it might not always be nice, it is never dull. Scandals, corruption allegations, conspiracy theories and hooliganism – every weekend seems to bring new controversy. Somehow, I can't help but get the impression that the Russians prefer it that way. After all, as Zinin admitted to me months before FC MVD died their very public death: "Predictability might be fine for the English, but it's hell for a Russian."

Postscript: the Prosecutor General has since confirmed that there are no grounds to suspect the stolen money was used to finance FC MVD

• Marc Bennetts is the author of Football Dynamo: Modern Russia and the People's Game (Virgin Books)